Mean Square Exponential Stability Research Articles

Impulsive stabilization of complex-valued stochastic complex networks via periodic self-triggered intermittent control

The aim of this article is to research the stabilization issue of complex-valued stochastic Markovian switching complex networks with time delays and time-varying multi-links (CSMCTM) via periodic self-triggered intermittent impulsive control (PSIIC). Thereinto, PSIIC is designed for the first time by combining intermittent impulsive control with periodic self-triggered control for intermittent control. It is worth emphasizing that the triggered protocol is designed to be more flexible, and easier to implement than previously reported triggered protocol. Then, by means of impulsive control, intermittent control, event-driven control theory and stability analysis, a stabilization criterion of CSMCTM in the sense of exponential stability in mean square is obtained. Whereafter, the stability of a class of complex-valued inertial neural networks is researched as a practical application of our theoretical results. Ultimately, a numerical example gives a corresponding verification.

On stability of solutions of stochastic delay differential equations

This paper addresses exponential stability of a class of stochastic delay differential equations and their numerical solutions. We begin by establishing criteria for exponential stability in mean square of stochastic delay differential equations. We then show that the Euler–Maruyama approximation method correctly reproduces exponential stability in mean square for sufficiently small step sizes. Consequently criteria for almost sure exponential stability of the exact and the Euler–Maruyama approximation are also obtained. In contrast to the advances in the literature, this work provides more accurate estimates of the Lyapunov exponents of stochastic delay differential equations and their Euler–Maruyama approximations.

Explicit criteria for exponential stability in mean square of stochastic difference systems with delays

Abstract By a novel approach, we present some new criteria for the exponential stability in mean square of solutions of non-linear stochastic difference systems with time-varying delays. A discussion of the obtained results is given. Illustrative examples and simulations are provided.

A novel approach to exponential stability in mean square of stochastic difference systems with delays

By a novel approach, we present in this paper for the first time, some explicit criteria for the exponential stability in mean square of solutions of general stochastic difference systems with time-varying delays. Both delay-independent and delay-dependent stability criteria are provided. A discussion and illustrative examples are given.

Membership-function-dependent memory controller design for interval type-2 fuzzy systems under fading channels

This paper studies the problem of membership-function-dependent memory output feedback (MOF) controller design for interval type-2 (IT2) fuzzy systems under fading channels. A time-varying stochastic process is introduced to model the unpredictable channel fading phenomenon. Taking the impact of channel fading into consideration, a non-parallel distribution compensation (non-PDC) strategy is employed to construct a class of memory output feedback fuzzy controllers. By fully exploiting the membership functions, the membership-function-dependent performance analysis and controller synthesis results have been obtained, such that the closed-loop system can be guaranteed with mean-square exponential stability and performance γ. Finally, simulation studies have been presented to demonstrate the effectiveness of the proposed approach.

Stabilization of Stochastic McKean--Vlasov Equations with Feedback Control Based on Discrete-Time State Observation

In this paper, we study the stability of solutions of stochastic McKean--Vlasov equations via feedback control based on discrete-time state observation. By using a specific Lyapunov function, the $H_{\infty}$ stability, asymptotic stability and exponential stability in mean square for the solution of the controlled systems are obtained. Since the distribution of the solution is difficult to observe, we study the corresponding particle system which can be observed for the feedback control. We prove that the exponential stability of control system is equivalent to the the exponential stability of the corresponding particle system. Finally, an example is provided to show the effectiveness of the theory.

Stability of neutral stochastic delayed systems with switching and distributed-delay dependent impulses

This paper is devoted to discuss the exponential stability in mean square of neutral stochastic delayed systems (NSDDs) with switching and distributed-delay dependent impulses. By using multiple Lyapunov functions and average dwell time (ADT), we provide some sufficient conditions for the exponential stability in mean square for NSDDs with switching and distributed-delay dependent impulses. Compared with the existing related works, we consider not only the influences of switches and neutral type on the stability of NSDDs with switching and distributed-delay dependent impulses but also the influences of both the stable continuous dynamics case and the stable discrete dynamics case. Finally, we provide two examples to illustrate the effectiveness of the theory.

Stability of the analytic solution and the partially truncated Euler–Maruyama method for a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients

In this paper, we develop the partially truncated Euler–Maruyama method of a class of stochastic Volterra integro-differential equations with non-globally Lipschitz continuous coefficients. The mean-square exponential stability and the mean-square stability of the analytic solution and the partially truncated Euler–Maruyama method are investigated. Moreover, the theoretical results are illustrated by some numerical examples.

Delay sampled-data stabilization of stochastic multi-weights networks with Lévy noise

This paper introduces a modified sampled-data control for solving the stabilized problem of stochastic complex multi-weights networks with time delay and Lévy noise, where the sampled states depend on a time varying delay. That is, we design a class of delay sampled-data control to stabilize the given stochastic complex multi-weights networks with time delay and Lévy noise in the sense of exponential stability in mean square. Using the Lyapunov method, graph theory, and some techniques of inequality, several types stabilized criteria are obtained. The control law is determined simultaneously, which depends on the perturbed intensity of noise, the coupling strength, time delays, and the lower and upper bounds of sampling intervals. In particular, as a practical application of our theoretical results, the stabilized problem of stochastic delayed oscillator networks with Lévy noise and multi-weights is researched, and the correlative numerical simulations are provided for illustration.

Event-Triggered Impulsive Control for Stochastic Networked Control Systems Under Cyber Attacks

The event-triggered impulsive control (ETIC) problem is studied for stochastic networked control systems (NCSs) under random cyber attacks. The random cyber-attacks model is proposed to integrate denial-of-service (DoS) attacks and deception attacks into a unified framework by means of two independent Bernoulli random sequences. In ETIC systems, the impulsive control time sequence is generated by the event-triggered mechanism (ETM). Both continuous ETM and periodic ETM are developed by continuous measuring and periodic sampling, respectively. In order to exclude the Zeno behavior, an easy and effective method is provided to choose the waiting time of continuous ETM and the sampling period of periodic ETM. According to the proposed ETMs, sufficient conditions of the mean-square exponential stability are derived for stochastic NCSs. An example of Chua’s circuits is given to explain our ETIC schemes.

Stochastic Epidemic Model for COVID-19 Transmission under Intervention Strategies in China

In this paper, we discuss an EIQJR model with stochastic perturbation. First, a globally positive solution of the proposed model has been discussed. In addition, the global asymptotic stability and exponential mean-square stability of the disease-free equilibrium have been proven under suitable conditions for our model. This means that the disease will die over time. We investigate the asymptotic behavior around the endemic equilibrium of the deterministic model to show when the disease will prevail. Constructing a suitable Lyapunov functional method is crucial to our investigation. Parameter estimations and numerical simulations are performed to depict the transmission process of COVID-19 pandemic in China and to support analytical results.

A3C-Based Intelligent Event-Triggering Control of Networked Nonlinear Unmanned Marine Vehicles Subject to Hybrid Attacks

This paper is concerned with the intelligent event-triggering-based positioning control of networked unmanned marine vehicle (UMV) systems with hybrid attacks, where the UMV and control station is connected by a communication network and the DoS attack and Deception attack are studied. Firstly, a stochastic switched Takagi-Sugeno (T-S) fuzzy system model is proposed for the networked nonlinear UMV systems subject to aperiodic DoS attack and random Deception attack. Then, a novel asynchronous advantage actor-critic (A3C) learning-based event-triggering approach is introduced to alleviate the communication load. By using the Lyapunov stability theory and switched system analysis method, the mean-square exponential stability condition of the closed-loop system and the design method of observer-based controller are devised. Finally, an example of a networked UMV system is given to verify the effectiveness of the proposed resilient control strategy.

Protocol-Based Output-Feedback Control for Semi-Markov Jump Systems

This study addresses the output-feedback control problem for general semi-Markov jump systems with a memory-dynamic event-triggered protocol. Based on the average dwell-time strategy, a novel framework of semi-Markov process subject to a higher level deterministic switching signal is constructed, where the Markov renewal process is nonhomogeneous. Aiming at improving communication efficiency and control performance, a novel dynamic-memory event-triggered protocol is proposed, and the resulting system can be transformed into a time-delay system. By considering an asynchronous memory-based output-feedback control law, whose asynchronization can be modeled by a nonhomogeneous hidden semi-Markov model, some parameter-dependent sufficient criteria are forwarded to ensure the mean-square exponential stability of the closed-loop system. Finally, the effectiveness and applicability of the presented approach are testified by two examples.

Mean-square stabilization of impulsive neural networks with mixed delays by non-fragile feedback involving random uncertainties

In this paper, we consider a class of neural networks with mixed delays and impulsive interferences. Firstly, a sufficient condition is given to ensure the existence and uniqueness of the equilibrium point of the proposed neural networks by employing the contraction mapping theorem. Secondly, we discuss the issue of the exponential stability in mean-square of the equilibrium point by a non-fragilely delayed output coupling feedback which involves stochastically occurring gain oscillations. The designed feedback input can be tolerant of limited stochastic fluctuations of control gains and be robust against potential errors caused by factors like round-off. By combining methods of Lyapunov–Krasovskii functional and free-weighting matrix, a delay-dependent output coupling feedback with stochastically occurring uncertainties is designed and linear-matrix-inequalities(LMIs)-based sufficient conditions for the exponential stabilization in mean square are derived. Finally, three numerical examples are presented to illustrate the feasibility of theoretical results with a benchmark real-world problem.

Stability of switched stochastic reaction–diffusion systems

As one of important hybrid dynamical systems, switched system has practical applications in some practical systems. Generally, switched system is made up of a family of continuous-time subsystems and discrete switching signals. Affected by environmental disturbance, stochastic switched system should be considered. This paper deals with a class of switched stochastic reaction-diffusion systems (SSRDSs, in short), where the discrete switching signal is a right continuous and piecewise function. The switching instants are stopping times or deterministic times. Criterions on stability in probability and exponential stability in mean square of the trivial solution for SSRDSs are derived by means of Lyapunov functional methods. We propose two examples to verify the obtained theoretical results.

Stabilization of stochastic coupled systems with Lévy noise and regime switching diffusions via intermittent control with a time delay

In this paper, the stabilization problem of stochastic Lévy noise coupled systems with time delays and regime switching diffusions (SLCSTR) is researched via intermittent control with a time delay (ICTD). It is worth pointing out that both Lévy noise and regime switching diffusions are considered into coupled systems. Furthermore, different from previous intermittent control based on current state, ICTD combining the benefits of aperiodically intermittent control and delay feedback control is based on past state. Meanwhile, the stabilization problem of SLCSTR is investigated via delay feedback control. Then, by Lyapunov method, graph theory and some techniques of inequalities, some stabilization criteria of SLCSTR in the sense of exponential stability in mean square are obtained. In addition, we investigate the stabilization problem of stochastic delayed coupled oscillators with Lévy noise and regime switching diffusions as a practical application of our theoretical results. Finally, numerical simulations are given for illustration.

Output-feedback control for stochastic impulsive systems under Round-Robin protocol

In this paper, an output-feedback control problem is investigated for a class of stochastic systems with impulsive effects under Round-Robin (RR) protocol. First, the RR protocol is exploited for the purpose of effectively relieving communication burden, and energy-saving. The considered stochastic impulsive system is essentially as a switched impulsive one due mainly to the switching feature of the RR protocol. Next, an extended comparison principle (ECP) of the stochastic impulsive systems is developed to handle the effects from both the switching and impulsive signals. By means of this ECP, sufficient conditions are derived to guarantee the exponential mean-square stability of the stochastic switched impulsive system, and then the output-feedback controller is designed through solving a set of semi-definite programming problems. Finally, an example is given to illustrate the effectiveness and applicability of the proposed control scheme.

Formation Tracking Control of Networked Systems With Time-Varying Delays and Sampling Under Fixed and Markovian Switching Topology

This article studies the formation tracking control (FTC) of nonlinear second-order leader&#x2013;following multiagent systems (LFMASs) with time-varying delays and periodic sampling. The FTC protocols based on position and velocity information of neighbor agents and measurable communication noise in fixed and Markovian switching directed topology are proposed. Some sufficient conditions are obtained to reach formation tracking by using the algebraic graph theory and generalized Halanay inequality. Meanwhile, the upper bound of formation-able time-varying delays <inline-formula><tex-math notation="LaTeX">$\bar{\tau }$</tex-math></inline-formula> is obtained. Results show that the LFMASs can achieve formation tracking in mean-square exponential stability as well as almost sure exponential stability under the proposed control algorithms. Finally, the availability of the theoretical results is verified by numerical simulation.

Mean-square exponential stability of impulsive conformable fractional stochastic differential system with application on epidemic model

The main objective of this paper is to analyze the exponential stability of a new problem of an n-dimensional non-linear impulsive conformable stochastic differential system with the various fractional orders. By applying the conversion of the state variable, the solution of the aimed impulsive stochastic differential system is related to the corresponding solution of the non-impulsive system. Then the sufficient conditions for the exponential stability of the proposed impulsive system are accomplished by obtaining sufficient conditions for the exponential stability of the respective non-impulsive system. The novelty of this work is that the Razumikhin stability technique (without using the Lyapunov function) is used to achieve the stability conditions for the impulsive conformable stochastic system. The gained theoretical conclusions are confirmed by applying the conformable stochastic SIR epidemic model with impulsive immigration. Finally, the influence of fractional orders in the dynamical performance of the impulsive conformable stochastic SIR epidemic model is illustrated with graphical representations.

Fuzzy multi-objective fault-tolerant control for nonlinear Markov jump singularly perturbed systems with persistent dwell-time switched transition probabilities

This paper studies the discrete-time slow state feedback fault-tolerant controller design issue for Takagi-Sugeno fuzzy-model-based Markov jump singularly perturbed nonlinear systems, in which transition probabilities of systems subject to persistent dwell-time switching mechanism. In order to eliminate the influence of actuator faults and provide a more flexible control strategy, a multi-objective fault-tolerant controller is designed to ensure the stability of the system and meet the requirements of various performance indexes. The goal is to establish some sufficient conditions, which ensure the mean-square exponential stability and the extended dissipativity performance of the closed-loop system. Furthermore, the gains of the designed controller can be obtained by solving the problem of convex optimization. Finally, the availability of the designed controller is demonstrated by a numerical example and a tunnel diode circuit system.